Load balancing-the allocation of work across parallel resources to reduce delay, energy and cost-is a pervasive challenge in science and engineering, from large-scale simulation and data processing to cloud and manufacturing operations. Motivated by the emerging bottleneck in large language model (LLM) serving, we study a particularly stringent regime of load balancing that arises in barrier-synchronized, stateful systems: work cannot be freely migrated and progress is gated by the slowest participant at each step, so heterogeneity and temporal drift in workloads create persistent stragglers and substantial idle time. LLM serving under data-parallel decoding provides a prominent modern instance: in production traces, barrier-induced idle can exceed 40% of compute time per decode step. Here we develop a universal load-balancing principle, which admits a step-wise finite-horizon integer-optimization formulation and yields worst-case guarantees: across LLM decode models and a broader class of non-decreasing workload drift processes, it reduces long-run imbalance by a factor that grows with batch size and system scale. Extensive experiments corroborate the theory, showing substantial improvements in throughput and latency together with reductions in energy consumption. These results provide a general, theoretically grounded framework for load balancing, with immediate implications for sustainable LLM serving and broad relevance to other synchronization-gated resource-allocation problems.

Imbalanced classification, where one class is observed far less frequently than the other, often causes standard training procedures to prioritize the majority class and perform poorly on rare but important cases. A classic and widely used remedy is to augment the minority class with synthetic examples, but two basic questions remain under-resolved: when does synthetic augmentation actually help, and how many synthetic samples should be generated? We develop a unified statistical framework for synthetic augmentation in imbalanced learning, studying models trained on imbalanced data augmented with synthetic minority samples and evaluated under the balanced population risk. Our theory shows that synthetic data is not always beneficial. In a ``local symmetry" regime, imbalance is not the dominant source of error near the balanced optimum, so adding synthetic samples cannot improve learning rates and can even degrade performance by amplifying generator mismatch. When augmentation can help (a ``local asymmetry" regime), the optimal synthetic size depends on generator accuracy and on whether the generator's residual mismatch is directionally aligned with the intrinsic majority-minority shift. This structure can make the best synthetic size deviate from naive full balancing, sometimes by a small refinement and sometimes substantially when generator bias is systematic. Practically, we recommend Validation-Tuned Synthetic Size (VTSS): select the synthetic size by minimizing balanced validation loss over a range centered near the fully balanced baseline, while allowing meaningful departures when the data indicate them. Simulations and a real sepsis prediction study support the theory and illustrate when synthetic augmentation helps, when it cannot, and how to tune its quantity effectively.

Class imbalance significantly degrades classification performance, yet its effects are rarely analyzed from a unified theoretical perspective. We propose a principled framework based on three fundamental scales: the imbalance coefficient $η$, the sample--dimension ratio $κ$, and the intrinsic separability $Δ$. Starting from the Gaussian Bayes classifier, we derive closed-form Bayes errors and show how imbalance shifts the discriminant boundary, yielding a deterioration slope that predicts four regimes: Normal, Mild, Extreme, and Catastrophic. Using a balanced high-dimensional genomic dataset, we vary only $η$ while keeping $κ$ and $Δ$ fixed. Across parametric and non-parametric models, empirical degradation closely follows theoretical predictions: minority Recall collapses once $\log(η)$ exceeds $Δ\sqrtκ$, Precision increases asymmetrically, and F1-score and PR-AUC decline in line with the predicted regimes. These results show that the triplet $(η,κ,Δ)$ provides a model-agnostic, geometrically grounded explanation of imbalance-induced deterioration.

The balanced loss is a widely adopted objective for multi-class classification under class imbalance. By assigning equal importance to all classes, regardless of their frequency, it promotes fairness and ensures that minority classes are not overlooked. However, directly minimizing the balanced classification loss is typically intractable, which makes the design of effective surrogate losses a central question. This paper introduces and studies two advanced surrogate loss families: Generalized Logit-Adjusted (GLA) loss functions and Generalized Class-Aware weighted (GCA) losses. GLA losses generalize Logit-Adjusted losses, which shift logits based on class priors, to the broader general cross-entropy loss family. GCA loss functions extend the standard class-weighted losses, which scale losses inversely by class frequency, by incorporating class-dependent confidence margins and extending them to the general cross-entropy family. We present a comprehensive theoretical analysis of consistency for both loss families. We show that GLA losses are Bayes-consistent, but only $H$-consistent for complete (i.e., unbounded) hypothesis sets. Moreover, their $H$-consistency bounds depend inversely on the minimum class probability, scaling at least as $1/\mathsf p_{\min}$. In contrast, GCA losses are $H$-consistent for any hypothesis set that is bounded or complete, with $H$-consistency bounds that scale more favorably as $1/\sqrt{\mathsf p_{\min}}$, offering significantly stronger theoretical guarantees in imbalanced settings. We report the results of experiments demonstrating that, empirically, both the GCA losses with calibrated class-dependent confidence margins and GLA losses can greatly outperform straightforward class-weighted losses as well as the LA losses. GLA generally performs slightly better in common benchmarks, whereas GCA exhibits a slight edge in highly imbalanced settings.

The widespread success of deep learning models today is owed to the curation of extensive datasets significant in size and complexity. However, such models frequently pick up inherent biases in the data during the training process, leading to unreliable predictions. Diagnosing and debiasing datasets is thus a necessity to ensure reliable model performance.

Semantic segmentation datasets often exhibit two types of imbalance: \textit{class imbalance}, where some classes appear more frequently than others and \textit{size imbalance}, where some objects occupy more pixels than others. This causes traditional evaluation metrics to be biased towards \textit{majority classes} (e.g.

The class imbalance problem, as an important issue in learning node representations, has drawn increasing attention from the community. Although the imbalance considered by existing studies roots from the unequal quantity of labeled examples in different classes (quantity imbalance), we argue that graph data expose a unique source of imbalance from the asymmetric topological properties of the labeled nodes, i.e., labeled nodes are not equal in terms of their structural role in the graph (topology imbalance).

Dealing with severe class imbalance poses a major challenge for many real-world applications, especially when the accurate classification and generalization of minority classes are of primary interest.In computer vision and NLP, learning from datasets with long-tail behavior is a recurring theme, especially for naturally occurring labels. Existing solutions mostly appeal to sampling or weighting adjustments to alleviate the extreme imbalance, or impose inductive bias to prioritize generalizable associations. Here we take a novel perspective to promote sample efficiency and model generalization based on the invariance principles of causality. Our contribution posits a meta-distributional scenario, where the causal generating mechanism for label-conditional features is invariant across different labels. Such causal assumption enables efficient knowledge transfer from the dominant classes to their under-represented counterparts, even if their feature distributions show apparent disparities. This allows us to leverage a causal data augmentation procedure to enlarge the representation of minority classes. Our development is orthogonal to the existing imbalanced data learning techniques thus can be seamlessly integrated. The proposed approach is validated on an extensive set of synthetic and real-world tasks against state-of-the-art solutions.